p-Geodesic transformations and their groups in second-order tangent bundles induced by concircular transformations of bases

We investigate the flattening properties of the Lie group $G_r^{II}$ of transformations of a second-order tangent bundle $T^2(M)$ equipped with the lift $∇^{II}$ of an affine connection $∇$ and the lift $g^{II}$ of a metric $g$ on the base of $M$ induced by the Lie group $G_r$ of concircular transformations of the base of $M$. The obtained results reveal certain geometric features of the induced group $G_r^{II}$ within the framework of the theory of $p$-geodesic mappings.